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The model of a photoacoustic gas-microphone signal in the time domain recorded in a transmission configuration using a minimum volume cell is derived. This model takes into account the inertial thermal relaxations of both the sample and the gas filling the cell by means of the generalized hyperbolic theory of heat conduction. With the introduction of electro-thermal analogy for the thin sample and short microphone length cavity, characteristic quantities are defined, which can be used in solving the inverse problem in time-domain photoacoustic in both cases, when thermal relaxations are neglected as well as when they are considered. The derived model that includes thermal relaxation explains the experimentally observed occurrence of overshoots and undershoots as well as an oscillatory approach to the steady values of the recorded signal in high-resolution time-domain photoacoustic measurements of thin semiconductor membranes, which will be presented in detail in Paper II of the paper. © 2023 Author(s).

In order to make the photothermal effect detectable from a sample with low optical absorption, an optically opaque layer must be applied on its surface. A model of optically induced temperature variations for such a structure is derived, with a very thin coating applied on the non-illuminated (back) side of the sample and neglecting heat flux dissipation in the coating. Validation of the model is performed by comparing the obtained results with the results for the corresponding two-layer structure model. The influence of optical absorption on surface temperature variations of both optically transparent and semi-transparent film, whether the film is a good or poor thermal conductor, is analyzed. It is shown that the effects of optical absorption in the coated structure can be observed through variations in the measured temperature, despite the low absorbance of the sample.

In this paper, the influence of the input and output data scaling and normalization on the neural network overall performances is investigated aimed at inverse problem-solving in photoacoustics of semiconductors. The logarithmic scaling of the photoacoustic signal amplitudes as input data and numerical scaling of the sample thermal parameters as output data are presented as useful tools trying to reach maximal network precision. Max and min–max normalizations to the input data are presented to change their numerical values in the dataset to common scales, without distorting differences. It was demonstrated in theory that the largest network prediction error of all targeted parameters is obtained by a network with non-scaled output data. Also, it was found out that the best network prediction was achieved with min–max normalization of the input data and network predicted output data scale within the range of [1–10]. Network training and prediction performances analyzed with experimental input data show that the benefits and improvements of input and output scaling and normalization are not guaranteed but are strongly dependent on a specific problem to be solved.

In this paper, a self-consistent inverse procedure is developed for the estimation of linear thermal expansion coefficient and thermal diffusivity of solids from transmission photoacoustic measurement. This procedure consists of two single-parameter fitting processes applied alternately: phase data are fitted by shifting thermal diffusion coefficient, while amplitude data are fitted by shifting thermal expansion coefficient. Each fitting process uses the resulting parameter of the other, previously finished one, thus converging to the best solution-pair achievable. In numerical experiments, the convergence proves to be very fast. The achieved parameter estimation error is as low as 1%, and it can be lowered further more by increasing the fitting resolution in parameter space. The application of the procedure on experimentally obtained aluminum photoacoustic response (measurements) on three thickness levels returns the estimates of its thermal diffusion and thermal expansion coefficients within expected literature boundaries.

This paper presents the model of surface temperature variations, resulting from the photothermal effect induced in a “thin film – highly absorbing surface layer” structure, where the thin film is irradiated. The influence of the optical absorption coefficient and sample thickness on the induced temperature gradient is analyzed. It is shown that, depending on the product of these parameters (optical absorbance) in the described structure, the phenomenon of inverse temperature gradient can occur, further influencing the direction and the magnitude of thermoelastic displacement., U radu je prikazan model koji opisuje površinske temperaturske varijacije nastale kao posledica fototermalnog efekta u strukturi tanki film – prevlaka sa visokim koeficijentom optičke apsorpcije, gde je obasjan tanki film. Analiziran je uticaj koeficijenta optičke apsorpcije i debljine uzorka na indukovani gradijent temperature. Pokazano je da u zavisnosti od proizvoda koeficijenta optičke apsorpcije i debljine uzorka (apsorbanse uzorka), u takvoj strukturi može doći do formiranja inverznog temperaturskog gradijenta, što utiče na smer i veličinu termoelastičnog pomeraja.

In our previous articles [1,2] we have shown that the application of artificial neural networks (ANNs) in photoacoustics could improve experimental procedures in many ways: better accuracy and precision in investigated sample parameters prediction, better control of the experimental conditions together with approaching to the real-time characterization of the investigated sample, etc. Here we will try to show why the different types of scaling and normalization procedures could be beneficial to the accuracy, precision and numerical stability of the network predicted parameters and network training speed. To do that numerical (Fig.1) or logarithmic scaling and min-max and max normalizations are applied on experimental input data used in the ANNs training process. At the same time, specific numerical scaling is used for network output data (predicted sample thermal and geometric parameters such as thermal diffusivity, linear coefficient of thermal expansion, thickness) to find possible benefits to ANNs performances. Our analysis of training, stability, and accuracy of network prediction will rely on the ANNs trained with or without scaling and/or normalization to find their influence on overall network performances.

This paper introduces the possibility of the determination of optical absorption and reflexivity coefficient of silicon samples using neural networks and reverse-back procedure based on the photoacoustics response in the frequency domain. Differences between neural network predictions and parameters obtained with standard photoacoustic signal correction procedures are used to adjust our experimental set-up due to the instability of the optical excitation source and the state (contamination) of the illuminated surface. It has been shown that the changes of the optical absorption values correspond to the light source wavelength fluctuations, while changes in the reflexivity coefficient, obtained in this way, correspond to the small effect of the ultrathin layer formation of SiO2 due to the natural process of surface oxidation.

In this article, a method for determination of photoacoustic detector transfer function as an accurate representation of microphone frequency response is presented. The method is based on supervised machine learning techniques, classification and regression, performed by two artificial neural networks. The transfer function is obtained by determining the microphone type and characteristic parameters closely related to its filtering properties. This knowledge is crucial within the signal correction procedure. The method is carefully designed in order to maintain requirements of photoacoustic experiment accuracy, reliability and real-time performance. The networks training is performed using large base of theoretical signals simulating frequency response of three types of commercial electret microphones frequently used in photoacoustic measurements extended with possible flat response of the so-called ideal microphone. The method test is performed with simulated and experimental signals assuming the usage of open-cell photoacoustic set-up. Experimental testing leads to the microphone transfer function determination used to correct the experimental signals, targeting the “true” undistorted photoacoustic response which can be further used in material characterization process.

In this paper, a methodology for the application of neural networks in phase-match calibration of gas–microphone photoacoustics in frequency domain is developed. A two-layer deep neural network is used to determine, in real-time, reliably and accurately, the phase transfer function of the used microphone, applying the photoacoustic response of aluminum as reference material. This transfer function was used to correct the photoacoustic response of laser-sintered polyamide and to compare it with theoretical predictions. The obtained degree of correlation of the corrected and theoretical signal tells us that our method of phase-match calibration in photoacoustics can be generalized to a photoacoustic response coming from a solid sample made of different materials.

In this work, theoretically/mathematically simulated models are derived for the photoacoustic (PA) frequency response of both volume and surface optically-absorbing samples in a minimum volume PA cell. In the derivation process, the thermal memory influence of both the sample and the air of the gas column are accounted for, as well as the influence of the measurement chain. Within the analysis of the TMS model, the influence of optical, thermal, and elastic properties of the sample was investigated. This analysis revealed that some of the processes, characterized by certain sample properties, exert their dominance only in limited modulation frequency ranges, which are shown to be dependent upon the choice of the sample material and its thickness. Based on the described analysis, two methods are developed for TMS model parameter determination, i.e., sample properties which dominantly influence the PA response in the measurement range: a self-consistent procedure for solving the exponential problems of mathematical physics, and a well-trained three-layer perceptron with back propagation, based upon theory of neural networks. The results of the application of both inverse problem solving methods are compared and discussed. The first method is shown to have the advantage in the number of properties which are determined, while the second one is advantageous in gaining high accuracy in the determination of thermal diffusivity, explicitly. Finally, the execution of inverse PA problem is implemented on experimental measurements performed on macromolecule samples, the results are discussed, and the most important conclusions are derived and presented.

Artificial neural networks as machine learning techniques have proven to be suitable tools for intelligent decision making. This paper presents the application of artificial neural networks for fast and precise characterization of electret microphones by photoacoustic measurements based on optical generation of sound. The transfer function of this type of devices is usually not determined precisely enough by the producers, especially phase transfer function, because such detectors are not widely applied in scientific experiments but are rather used in audio techniques where amplitude transfer function is more important. The distorted photoacoustic experimental signal, influenced by the measurement set-up in a non-linear manner, represents the input of our model, while the outputs are the detector characteristics. The model consists of two neural networks: the first one for the classification of the detector type and the second one for the determination of the detector parameters, related to its electronic and geometric features. Based on this approach and the theoretical model, relying on the acoustics of small volumes, the parameters and transfer characteristics for several microphones are obtained and compared to the characteristics provided by their producers. It has been shown that the suggested method results in much better detector characterization than the one provided in the official specifications. This could be significant not only for scientific applications of microphones but also for their design and applications in audio techniques.

Фотоакустичке мерне методе се интензивно развијају у последње четири децeнијеи налазе све разноврснију примену у науци, техници, медицини и стоматологији:од истраживања везе између структуре материје и њених термалних, еластичних,оптичких, електричних и других физичких особина, посебно на ниској временској(испод 0,1 милисекунде) и просторној скали (субмикронској), прекокарактеризације наноелектронских направа и фотонских кристала, па све до invivo дијагностике у медицини..., Photoacoustic (PA) measurement methods have been intensively developed in the lastfour decades and have found versatile application in science, technique, medicine anddentistry: from explorations of the relationship between structure of matter and itsthermal, elastic, optical, electrical and other physical properties (especially at low timescale– under 0.1 ms and small space-frame – submicron), through characterization ofnanoelectronic devices and photon crystals, all the way to in vivo diagnostics inmedicine...

In this work, thermal diffusivity of crystalline high-density polyethylene samples of various thickness, and prepared using different procedures, was evaluated by transmission gas-microphone frequency photoacoustics. The samples composition analysis and their degree of crystallinity were determined from the wide-angle X-ray diffraction, which confirmed that high-density polyethylene samples, obtained by slow and fast cooling, were equivalent in composition but with different degrees of crystallinity. Structural analysis, performed by differential scanning calorimetry, demonstrated that all of the used samples had different levels of crystallinity, depending not only on the preparing procedure, but also on sample thickness. Therefore, in order to evaluate the samples thermal diffusivity, it was necessary to modify standard photoacoustic fitting procedures (based on the normalization of photoacoustic amplitude and phase characteristics on two thickness levels) for the interpretation of photoacoustic measurements. The calculated values of thermal diffusivity were in the range of the expected literature values. Besides that, the obtained results indicate the unexpected correlation between the values of thermal diffusivity and thermal conductivity with the degree of crystallinity of the investigated geometrically thin samples. The results indicate the necessity of additional investigation of energy transport in macromolecular systems, as well as the possible employment of the photoacoustic techniques in order to clarify its mechanism.

In this paper, the models of surface temperature variations have been derived. Based on these models, photoacoustic (PA) response has been commented for transmission PA setup configurations of two-layer optically transparent samples, including the impact of finite heat propagation velocity through both layers (thermal memory) and the existence of volume absorption in both layers. By analyzing the derived model it has been shown that many parameters influence the photoacoustic response. Based on the derived model, some approximations have been discussed in order to enable the development of more accurate inverse solutions of photoacoustic problem, and the estimation of optical, thermal and other related physical properties of versatile materials. By using specific two-layer structure that consist of aluminum sample coated with layer of color dye, used in some photoacoustic experimental investigations, the influence of thermal memory properties of either the sample or the coating has been discussed. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

The influence of multiple optical reflexions on optically generated surface temperature variations has scarcely been considered throughout the literature. In this work, a model of optically generated heat sources in the sample with low optical absorption coefficient is derived. Multiple optical reflexions are considered at both surfaces of the sample exposed to the intensity-modulated laser beam. The impacts of the reflexion coefficient, the absorption coefficient and the thickness of the sample on the amplitude characteristics of photothermal responses are discussed.

A minimum volume photoacoustic (PA) cell, employed as an acoustic resonator, is presented. A model of the PA cell transfer function, as a combination of two Helmholtz resonators, is derived. Frequency PA response is described as the product of theoretically derived pressure variation and the transfer function of the PA cell. The derived model is applied to the frequency PA measurements, performed on laser-sintered polyamide. It is shown that the derived model explains the occurrence of resonant peaks in the high-frequency domain ( GT 10 kHz), in both amplitude and phase measurements, obtained by a gas-microphone minimal volume PA cell. The implementation of the model in the growing possibilities of sample characterization using gas-microphone PA cell is discussed.

In the present study, the possibility for the application of TiO2 nanocrystals of various shapes and sizes, for substrate-assisted laser desorption and ionization time-of-flight mass spectrometric (SALDI TOF MS) quantitative analysis of small molecules (steroid hormones, amino acids and saccharides) was investigated. Parameters, such as homogeneity of the substrate/analyte distribution, reproducibility of the measurements, within-day, and day-to-day repeatability, were determined. The homogeneity of different nanocrystal/analyte combinations on the target plate were compared based on the signal-to-noise values of several analyte signals. Obtained results show that all TiO2 nanocrystals, regardless of their shape, have great potential for the detection and determination of steroid hormones, amino acids and saccharides with good analytical parameters and detection limits. On the other hand, the reproducibility of the S/N ratio and detectability of the analytes recorded in various modes differ depending on the substrate. All examined molecules were detectable in negative ion mode with TiO2 NTs, in contrast to all other organic matrices and substrates, and the best reproducibility was obtained with the larger nanocrystals, TiO2 PNSs and TiO2 NTs, making them good candidates for the quantitative determination of small molecules.

On the basis of the generalized photoacoustic response model, which includes the influence of thermal memory on both thermoconducting and thermoelastic components, photoacoustic response of thin films is analysed. It is demonstrated that the influence of thermal memory is manifested at frequencies above certain boundary frequency, which depends on thermal memory properties of the sample and its depth. A linear relation, linking heat propagation velocity and measured signal, is derived. Taking into account the confinement of the frequency range imposed by the measuring system, it is indicated that thermal memory properties of non-cristaline thin films can be determined in a photoacoustic experiment.

Photothermal thermoelastic bending depends on an optically generated dynamic thermal field distribution within a sample. A generalized description of the distribution is proposed, including the effects of a finite heat propagation velocity and a finite, non-zero time of thermal relaxation (known as thermal memory effects in generalized heat conduction theory), and finally the generated thermoelastic bending is calculated by using both a thin solid-plate approximation and a decoupling system of thermoelastic equations. The comparison between this model and the classical one, which does not account for thermal memory influence, has been made. If the sample is thicker than the value of its minimal thermal diffusion length, the difference between the two models becomes insignificant. Otherwise, it has been shown that the two models tend to overlap at low and high modulation frequencies of the excitation light, while in the mid-frequency range, some deviations become more apparent and thermal memory properties of the sample must be taken into account. The suggested model enables evaluation of thermal memory properties for such a solid.

In this paper, a model of the thermoconducting component of the indirect photoacoustic (PA) response is derived that includes thermal memory properties of the examined material and its fluid environment. A comparison is made between the derived model and the classic one, which neglects the influence of thermal memory. It has been shown that, at modulation frequencies lower than a certain boundary frequency of the light source, these models tend to overlap, while at higher frequencies, noticeable differences occur. The boundary frequency depends on heat propagation velocity through the sample and its thickness. This observation limits the validity domain of previous models to a range lower than the boundary frequency, offering, at the same time, the possibility of obtaining thermal memory properties using PA effects at frequencies above it.

In this study, a model of thermoconducting components of the transmission photoacoustic response is analyzed, which includes thermal memory properties of both the examined solid sample and its fluid environment. It is shown that, at low modulation frequencies, lower than minimum among the inverse thermal relaxation time of air, the inverse thermal relaxation time of the sample, and the certain frequency at which the sample is thinner than one-quarter of the wavelength of time-varying temperature perturbation, thermal memory does not affect the photoacoustic response, while, at high frequencies, noticeable effects are observed. These results indicate the possibility of evaluating thermal memory properties of solid samples using classical, transmission, high frequency photoacoustic measurements.

In this work, the thermoelastic component of the photoacoustic response is derived, including the thermal memory of the material. The comparison between this model and the classic one, which does not account for the influence of thermal memory is made. It has been noticed that the two models tend to overlap at very high and very low frequencies of the light modulation spectrum, while in the middle range some deviations become more apparent, which proves that thermal memory must be taken into account. It has also been shown that the limits of this range are the function of heat propagation velocity and thickness of the sample. Based upon the processing of obtained data, it has been concluded that the characteristics of the output signal, in the range of the interest, are highly influenced by thermal dynamic qualities, like heat diffusivity and thermal relaxation time, as well as the sample thickness.